阅读说明：本技术 航磁数据向下延拓方法 (Aeromagnetic data downward continuation method ) 是由 张冲 吕庆田 徐志伍 赵金花 张代磊 袁文真 袁志明 崔明飞 于 2020-05-29 设计创作，主要内容包括：本发明提供了一种航磁数据向下延拓方法。该技术包括：对观测面的航磁垂向导数进行向上延拓,得到分布在观测面以上,七个不同高度的航磁垂向导数；利用观测面的航磁数据、航磁垂向导数以及其向上延拓七个高度的航磁垂向导数,构成向下延拓的八阶Adams-Bashforth格式；利用八阶Adams-Bashforth格式计算航磁数据的向下延拓初步结果；利用积分迭代方式,对向下延拓初步结果进行迭代,计算向下延拓最终结果。本发明提供的航磁数据向下延拓方法在保证准确和稳定的前提下,提高了向下延拓的深度,对航空磁测数据具有增强的效果,进而实现航磁数据解释的精细化改善。(The invention provides a method for downwardly extending aeromagnetic data. The technology comprises the following steps: carrying out upward continuation on the aeromagnetic vertical derivative of the observation surface to obtain seven aeromagnetic vertical derivatives which are distributed above the observation surface and have different heights; forming a downward continuation eighth-order Adams-Bashforth format by using aeromagnetic data of an observation surface, aeromagnetic vertical derivatives and aeromagnetic vertical derivatives extending upwards for seven heights; calculating a downward continuation preliminary result of aeromagnetic data by using an eighth-order Adams-Bashforth format; and iterating the downward continuation preliminary result by using an integral iteration mode, and calculating a downward continuation final result. The method for downwardly extending aeromagnetic data provided by the invention improves the depth of downwardly extending on the premise of ensuring accuracy and stability, has an enhanced effect on aeromagnetic data, and further realizes the fine improvement of aeromagnetic data interpretation.)

1. A method for downwardly extending aeromagnetic data is characterized by comprising the following steps:

carrying out upward continuation on the aeromagnetic vertical derivative of the observation surface to obtain seven aeromagnetic vertical derivatives which are distributed above the observation surface and have different heights;

forming a downward continuation eighth-order Adams-Bashforth format by using aeromagnetic data of an observation surface, aeromagnetic vertical derivatives and aeromagnetic vertical derivatives extending upwards for seven heights;

calculating a downward continuation preliminary result of aeromagnetic data by using an eighth-order Adams-Bashforth format;

and iterating the downward continuation preliminary result by using an integral iteration mode, and calculating a downward continuation final result.

2. The method of claim 1, wherein the eighth order Adams-bashfforth format is represented by the following formula:

wherein u is_z(x,y,z₀+h)、u_z(x,y,z₀+2h)、u_z(x,y,z₀+3h)、u_z(x,y,z₀+4h)、u_z(x,y,z₀+5h)、u_z(x,y,z₀+6h)、u_z(x,y,z₀+7h) is z₀Height h, 2h. Seven aeromagnetic vertical derivatives with different heights of 3h, 4h, 5h, 6h and 7h, h represents the extension height, z₀Representing the z-axis coordinates of the observation plane.

3. The method of claim 1, wherein iterating the downward continuation preliminary result by an integral iteration method to obtain a downward continuation final result, comprises:

taking the obtained result of the downward continuation of the eighth-order Adams-Bashforth format as an iteration initial value u (x, y, z) at the height-h₀-h)₀Calculating the height z by upward continuation method₀The aeromagnetic data u (x, y, z) of the observation plane₀)₀Comparing the aeromagnetic data u (x, y, z) before and after iteration₀) And u (x, y, z)₀)₀Difference Δ u of (1)₀Will differ by Δ u₀Substituting into the downward continuation value u (x, y, z)₀-h)₀In the above process, the process is repeated until the difference Δ u between the aeromagnetic data before and after iteration₀The design requirements are met.

4. The method of claim 1 to 3, further comprising:

and obtaining the aeromagnetic vertical derivative of the observation surface before carrying out upward continuation on the aeromagnetic vertical derivative of the observation surface to obtain seven aeromagnetic vertical derivatives distributed above the observation surface and at different heights.

5. The method of claim 4, wherein obtaining the vertical derivative of the observation plane comprises:

judging whether the measured data of the aeromagnetic vertical derivative of the observation surface exists or not;

if yes, acquiring the aeromagnetic vertical derivative of the observation surface;

and if not, calculating the aeromagnetic vertical derivative of the observation surface by using an ISVD (inverse synthetic vapor deposition) method.

6. The method for extending aeromagnetic data downwards according to claim 5, wherein calculating the vertical derivative of the aeromagnetic of the observation surface by using an ISVD method comprises:

calculating scalar positions by using a wave number domain aeromagnetic data conversion method;

calculating a second derivative of the scalar bit in the horizontal direction by using a finite difference method;

the second vertical derivative of the scalar bit, i.e. the first vertical derivative of the bit field, is obtained using laplace's equation.

Technical Field

The invention relates to the technical field of exploration technology and engineering, in particular to a method for downwardly extending aeromagnetic data.

Background

The traditional ground magnetic method measurement mode is influenced by the restriction factors such as the ground surface condition and the like, the production operation is difficult to implement and the efficiency is not high. The aeromagnetic method measurement is to take manned airplanes, unmanned airplanes and the like as carrying platforms and utilize equipment such as a magnetometer and the like to carry out air flight and acquire geomagnetic field data. The aeromagnetic measurement can solve the complex surface problems of deserts, swamps, forests, mountains and the like of ground magnetic measurement, but the geomagnetic field exponentially attenuates along with the increase of the height, so that the information of the aeromagnetic data is reduced, the aeromagnetic data is reduced to the ground or a level surface, the information can be enhanced, and the attenuation effect is reduced. This reduction technique is called downward continuation. But the general method can not realize the downward continuation of the aeromagnetic data with stable large depth (more than 15 times of point distance). An integral iteration downward continuation method is proposed in 2006 in xu Shi, stable downward continuation can be realized on noiseless data, downward continuation point distance is large (even reaching 20 times of point distance), but due to the fact that an initial iteration formula used by the method is poor in approximation effect, iteration times are more, calculation efficiency is reduced, and noise accumulation is caused (Chenshengchang and Xiaopeng fly, 2007); the Zhanchong is equal to a three-order Adams-Bashforth downward continuation method provided in 2017, and a direct downward continuation formula is established by utilizing an actually measured vertical derivative and a numerical solution Adams-Bashforth format of a differential equation. However, the third-order Adams-Bashforth downward continuation method is not high in precision, and actually measured aeromagnetic vertical derivatives need to be used in the practical process.

Disclosure of Invention

The invention aims to provide a method for downwardly extending aeromagnetic data, which improves the depth of downwardly extending on the premise of ensuring accuracy and stability, has an enhanced effect on aeromagnetic data and further realizes the fine improvement of aeromagnetic data interpretation.

In order to solve the technical problem, the invention provides a method for extending aeromagnetic data downwards, which comprises the following steps: carrying out upward continuation on the aeromagnetic vertical derivative of the observation surface to obtain seven aeromagnetic vertical derivatives which are distributed above the observation surface and have different heights; forming a downward continuation eighth-order Adams-Bashforth format by using aeromagnetic data of an observation surface, aeromagnetic vertical derivatives and aeromagnetic vertical derivatives extending upwards for seven heights; calculating a downward continuation preliminary result of aeromagnetic data by using an eighth-order Adams-Bashforth format; and iterating the downward continuation preliminary result by using an integral iteration mode, and calculating a downward continuation final result.

In some embodiments, the eighth order Adams-Bashforth format is represented by the following formula:

wherein u is_z(x,y,z₀+h)、u_z(x,y,z₀+2h)、u_z(x,y,z₀+3h)、u_z(x,y,z₀+4h)、u_z(x,y,z₀+5h)、u_z(x,y,z₀+6h)、u_z(x,y,z₀+7h) is z₀Seven aeromagnetic vertical derivatives with different heights above the height h, 2h, 3h, 4h, 5h, 6h and 7h, wherein h represents the extension height, and z represents the extension height₀Representing the z-axis coordinates of the observation plane.

In some embodiments, iterating the downward continuation preliminary result by using an integral iteration method to obtain a downward continuation final result, including: taking the obtained result of the downward continuation of the eighth-order Adams-Bashforth format as an iteration initial value u (x, y, z) at the height-h₀-h)₀Calculating the height z by upward continuation method₀The aeromagnetic data u (x, y, z) of the observation plane₀)₀Comparing the aeromagnetic data u (x, y, z) before and after iteration₀) And u (x, y, z)₀)₀Difference Δ u of (1)₀Will differ by Δ u₀Substituting into the downward continuation value u (x, y, z)₀-h)₀In the above process, the process is repeated until the difference Δ u between the aeromagnetic data before and after iteration₀The design requirements are met.

In some embodiments, further comprising: and obtaining the aeromagnetic vertical derivative of the observation surface before carrying out upward continuation on the aeromagnetic vertical derivative of the observation surface to obtain seven aeromagnetic vertical derivatives distributed above the observation surface and at different heights.

In some embodiments, acquiring the aeromagnetic vertical derivative of the observation plane comprises: judging whether the measured data of the aeromagnetic vertical derivative of the observation surface exists or not; if yes, acquiring the aeromagnetic vertical derivative of the observation surface; and if not, calculating the aeromagnetic vertical derivative of the observation surface by using an ISVD (inverse synthetic vapor deposition) method.

In some embodiments, calculating the aeromagnetic vertical derivative of the observation plane using an ISVD method comprises: calculating scalar positions by using a wave number domain aeromagnetic data conversion method; calculating a second derivative of the scalar bit in the horizontal direction by using a finite difference method; the second vertical derivative of the scalar bit, i.e. the first vertical derivative of the bit field, is obtained using laplace's equation.

After adopting such design, the invention has at least the following advantages:

the invention adopts an eighth-order Adams-Bashforth format, expands the vertical derivative related in the formula from actual measurement to calculation by utilizing an integral second vertical derivative method (ISVD method), and finally realizes the downward continuation technology of the invention through an integral iteration method. The method realizes downward continuation of 20 times of point distance with simple calculation, relatively stable process and large depth.

Drawings

The foregoing is only an overview of the technical solutions of the present invention, and in order to make the technical solutions of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and the detailed description.

Fig. 1 is a flowchart of a method for extending aeromagnetic data downward according to an embodiment of the present invention.

Detailed Description

The preferred embodiments of the present invention will be described in conjunction with the accompanying drawings, and it will be understood that they are described herein for the purpose of illustration and explanation and not limitation.

At present, the three-order Adams-Bashforth downward continuation method realizes downward continuation with simple calculation, relatively stable process and 5-time point distance greater than the conventional depth, but the formula of the three-order Adams-Bashforth downward continuation method is a three-order display format, and the truncation error isWhere ω is the interval (z)₀,z₀+ h) unknown constant, A is constant, h³Represents the power of the third power of h,

represents the vertical third derivative of u (x, y, ω). Compared with the method, the calculation error is large, and the stage error of the current three-order display format Adams-Bashforth downward continuation method is larger than that of the eight-order display format Adams-Bashforth downward continuation method; meanwhile, the existing three-order Adams-Bashforth downward continuation method needs to utilize the actually measured aeromagnetic vertical derivative, and the actually measured vertical derivative is not easy to obtain in China; in addition, the current third-order Adams-Bashforth downward continuation method is directly calculated by using a formula.

The invention adopts an eighth-order Adams-Bashforth format as a downward continuation technology, expands the vertical derivative related in the formula from actual measurement to calculation by utilizing an integral second vertical derivative method (ISVD method), and finally realizes downward continuation by an iteration technology of an integral iteration method.

In order to solve the defects in the prior art, a method for extending aeromagnetic data downwards based on an Adams-Bashforth format is provided. Fig. 1 shows a technical solution of a method for extending aeromagnetic data downward. Referring to fig. 1, the specific steps of the technical scheme are as follows:

firstly, judging whether the aeromagnetic vertical derivative data is actually measured on an observation surface, and if not, calculating a vertical derivative value u by using an integral secondary vertical derivative method (ISVD method)_z(x,y,z₀) Such asIf the measured value is found, the aeromagnetic vertical derivative is the measured value u_z(x,y,z₀)；

Secondly, aeromagnetic vertical derivative (obtained by actual measurement or calculation) data u of the observation surface_z(x,y,z₀) Carrying out upward continuation to obtain seven aeromagnetic vertical derivatives u distributed above an observation surface and at different heights_z(x,y,z₀+h)，u_z(x,y,z₀+2h)，u_z(x,y,z₀+3h)，u_z(x,y,z₀+4h)，u_z(x,y,z₀+5h)，u_z(x,y,z₀+6h)，u_z(x,y,z₀+7h) data;

then, the aeromagnetic data u (x, y, z) of the observation plane are utilized₀) Aeromagnetic vertical derivative data u_z(x,y,z₀) And its data extending seven heights upwards, form a downward extending eight-order Adams-Bashforth format, i.e. u (x, y, z)₀-h)；

Finally, the obtained downward continuation eighth-order Adams-Bashforth format is used as an initial value u (x, y, z) of iteration₀-h)₀Calculating aeromagnetic data u (x, y, z) of observation surface by upward continuation method₀)₀Comparing the difference Deltau of the aeromagnetic data before and after iteration₀Will differ by Δ u₀Substituting into the downward continuation value u (x, y, z)₀-h)₀In the above process, the process is repeated until the difference Δ u between the aeromagnetic data before and after iteration₀And obtaining an improved result of the down continuation of the aeromagnetic data based on the Adams-Bashforth format until the design requirements are met.

The invention belongs to aeromagnetic measurement technology, realizes the process of reducing aeromagnetic data from aerial observation surface to ground (downward continuation), improves the depth of downward continuation on the premise of ensuring accuracy and stability, has enhanced effect on aeromagnetic data, and further realizes the fine improvement of aeromagnetic data interpretation.

The calculation process of the integral second vertical derivative method (ISVD method) in the step 1 is as follows:

firstly, u (x, y, z) is calculated by using an aeromagnetic data conversion method of a wave number domain₀) Scalar bit v (x, y, z)₀)：

Wherein u (x, y, z)₀) And v (x, y, z)₀) Respectively represent a height z₀H is a positive number indicating the extension height, F, F^-1Which represents the fourier transform of the signal,representing a wavenumber domain vertical integral operator.

Scalar bits v (x, y, z) are then calculated using finite difference methods₀) Second derivative in horizontal direction:

where Δ x, Δ y represent the sampling interval in the horizontal direction.

Finally, a scalar position v (x, y, z) is obtained by using a Laplace equation₀) The second vertical derivative of (1), i.e. the bit field u (x, y, z)₀) First order vertical derivative u of_z(x,y,z₀)：

u_z(x,y,z₀)＝v_zz(x,y,z₀)＝-[v_xx(x,y,z₀)+v_yy(x,y,z₀)](3)

The upward continuation involved in the step 2 is a conversion method of a wave number domain, and the data conversion relation at different heights is as follows:

and xi and eta are another expression of coordinates x and y, and in order to facilitate integral calculation, the Fourier transform is carried out on the formula (4) to obtain an upward continuation method of a wave number domain:

wherein k is_x,k_yRepresenting the wavenumber domain coordinate, U (k), corresponding to the spatial domain coordinate x, y_x,k_y,z₀) Is u (x, y, z)₀) Is expressed in the wave number domain of (a),

representing the wavenumber domain upward continuation operator.

In the step 2, the aeromagnetic vertical data with seven different heights extend upwards to have aeromagnetic vertical gradients with heights of h, 2h, 3h, 4h, 5h, 6h and 7 h:

the eighth order Adams-Bashforth format in step 3 above is:

u (x, y, z) is calculated in the step 4₀H) as initial value u (x, y, z) for the iteration₀-h)₀I.e. the magnetic field data for the downward continuation position (height-h). For the initial value u (x, y, z) of the iteration₀-h)₀Carry out upward continuation, i.e.

Obtaining the aeromagnetic data u (x, y, z) of the observation surface₀)₁Comparing the difference delta u between the magnetic data after iteration and the original magnetic data₁，

Δu₁＝u(x,y,z₀)-u(x,y,z₀)₁(9)

Will differ by Δ u₁Substituting into the downward continuation value u (x, y, z)₀-h)₀Obtaining the initial value u (x, y, z) of the second iteration₀-h)₁，

u(x,y,z₀-h)₁＝u(x,y,z₀-h)₀+Δu₁(10)

Repeating the iterative process from (8) to (10),until the difference Deltau of aeromagnetic data before and after iteration₁Until the design requirements are met, a smaller constant ξ, i.e., Δ u, is selected₁≤ξ。

And finally, based on the improved result of the downward continuation of the aeromagnetic data in the Adams-Bashforth format.

The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the present invention in any way, and it will be apparent to those skilled in the art that the above description of the present invention can be applied to various modifications, equivalent variations or modifications without departing from the spirit and scope of the present invention.